The ground ⁶S and excited ⁴L states of the Mn²⁺ ion are perturbed by the cubic crystalline field and mixed by the spin-orbit coupling. A two-phonon Raman process, second order in the orbit-lattice interaction, is found to contribute to the ground-state splitting. The theory is developed within the framework of Van Vleck's small-wave-vector averaging procedure for acoustic phonons. Both the zero-point vibrational contribution and the temperature-dependent parts are calculated and compared with experimental measurements in Mn²⁺-doped MgO. Good qualitative agreement between the theory and experiment is found but quantitative agreement is not obtained.
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Keshav N. Shrivastava (1969) studied this question.
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